The issues range from frustrating to scary to just amusing.
On the frustrating end, I've had FOs who have no sense of keeping track of fuel. See, down here at companies that don't actually make money hand over fist and don't have a mainline partner that pays for their gas, we tend to get dispatched with min fuel all the time. It's not usual to see about 1:15 of fuel available on landing. That may sound like a lot, but when you consider about 1/4th of that is actually unusable during pitch up maneuvers of above 8 degrees or so (ie, a normal go around) it's actually not that much. There have been several times where the FO showed not comprehension that we were in a situation where if one thing went wrong (getting a 360 vector off of BUNTS in PHL and getting slow to 170 knots requiring flaps coming out) we could be in trouble as far as fuel goes. Sure, a simple "unable" or "min fuel" may solve that problem, but without prompting, they'd have had no idea.
I did a flight three months ago where there was a large line of convective weather. We found a hole to slip through and the FO was flying much closer to the upwind cell than the downwind cell (which were both about the same size). We talked about it for a bit and I realized he had no concept of the fact that that the winds aloft will carry turbulence, hail and other nastiness away from a storm and giving the upwind cell a wider berth than the downwind cell is probably a better idea.
A more scary event (and this was with a 250 hour wonder hired in 2008, so not a recent "weak" new hire) involved a guy flying a visual approach from about 10 miles out, where he was vectored in underneath the glideslope. He was then cleared to a lower altitude but somehow managed to set the altitude bug for an altitude above us. He commanded the autopilot to start descending to the "lower" altitude, but with the bug set above us, the plane would never capture and we'd just continue down until we hit the ground. He armed the approach at the same time and we got horizontal capture of the localizer but with the GS well above us, that would never capture. I told him what had happened but he was SO lost that he didn't understand the situation. We were about 8 miles out at 1500 feet and I finally told him just to hand fly. He dumped the autopilot but still followed the FD downward. I finally told him to look out the window at the runway and PAPI (which had been in sight this entire time) and he didn't understand why there were 4 red when we were still well above the glideslope (which wasn't showing on his display because it was pegged to the top of the screen).
The worst though are guys that just won't take any advice. I try not to ever tell somebody how to fly, especially if they are new. I'll give suggestions, and if asked, critique stuff, but part of the flight instructor mindset I've carried over to the left seat is that the best way for somebody to learn is to make there own mistakes. Obviously there is a limit on how much of a mistake I can let somebody make with 50 or 70 people behind us, but the premise is still the same. Some guys however KNOW they know better than I do and will either just ignore me or even argue that they are doing it the right way. Because of our low fuel dispatch policy we try to do power idle descents a lot. We don't have actual VNAV in the plane so we are reliant on an advisory "snowflake" and out own mental math. I can't remember where we were going, but it was someplace out on the Gulf Coast and they gave us a discretionary descent from FL360 down to 4000 feet. We had about 150 knots of wind against us at altitude but I knew from the lower level wind readouts (and the surface wind at the airport) we were going to lose that along the way down. The FO set up for a 4.0 degree descent which is a bit steeper than our normal 3.0 rate but works out to a power idle descent some times. I told him that wind the winds decreasing our ground speed would increase as we descended and our required descent rate would increase. He just said "I've got it". He waited until the required descent rate was about 3800fpm and then started down. Of course the wind dropped about 100 knots at 30,000 feet and the required rate went to 4500fpm which meant he needed spoilers to keep the speed back (not a big deal in bigger planes but not really needed with good planing in the RJ) and was pinning the passengers to the ceiling for 20,000 feet. After we landed (we had to do a 360 to get down as well) he blamed the plane for being "slow to descend".
And on the funny side, I've had, on two occasions, an FO keep about 300 knots through 10K because approach as said "max forward airspeed" and he assumed this waived the 250 requirement. I also had an FO ask if the label that said "ditch" on a Jepp 10-9 plate was where they wanted you to ditch the airplane if you couldn't make the runway for some reason.
There are lots of really smart FOs out there and I fully expect that a new guy who isn't familiar with the operation and the aircraft is going to take a little hand holding at first. However, what I don't like is that when I brief an oddball approach down to mins and look over and ask if he's got any questions or additions, to see a glazed over expression on his face and realize that this is the first time he's ever for real shot a VOR approach with multiple stepdowns. I don't like when we are holding and I'm trying to figure out our bingo fuel numbers to feel like that guy in the other seat can't back up my equations because he has no concept of diverting and just sits there and shrugs when I ask if the number looks about right. I hate having a strange MX situation arise in flight and start talking through systems with the guy and realize that despite him passing a systems oral he really doesn't understand the hydraulic system at even a basic level and I am pretty much talking to myself.
